Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Can you explain the strategy for winning this game with any target?
In this problem we are looking at sets of parallel sticks that
cross each other. What is the least number of crossings you can
make? And the greatest?
Given the products of adjacent cells, can you complete this Sudoku?
An environment which simulates working with Cuisenaire rods.
List any 3 numbers. It is always possible to find a subset of
adjacent numbers that add up to a multiple of 3. Can you explain
why and prove it?
A student in a maths class was trying to get some information from
her teacher. She was given some clues and then the teacher ended by
saying, "Well, how old are they?"
Katie and Will have some balloons. Will's balloon burst at exactly
the same size as Katie's at the beginning of a puff. How many puffs
had Will done before his balloon burst?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Four of these clues are needed to find the chosen number on this
grid and four are true but do nothing to help in finding the
number. Can you sort out the clues and find the number?
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
There are a number of coins on a table.
One quarter of the coins show heads.
If I turn over 2 coins, then one third show heads. How many coins are there altogether?
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
Got It game for an adult and child. How can you play so that you know you will always win?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.
Is it possible to draw a 5-pointed star without taking your pencil
off the paper? Is it possible to draw a 6-pointed star in the same
way without taking your pen off?
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Can you complete this jigsaw of the multiplication square?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Are these statements always true, sometimes true or never true?
Becky created a number plumber which multiplies by 5 and subtracts
4. What do you notice about the numbers that it produces? Can you
explain your findings?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
If you have only four weights, where could you place them in order
to balance this equaliser?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
The clues for this Sudoku are the product of the numbers in adjacent squares.
An investigation that gives you the opportunity to make and justify
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?